I start by saying Roulette is a sucker’s game.
It tricks many people by including a slot for “zero” which does not count as odd, even, red or black.
So while betting red or even may seem like a 0.50 probability of success, it is actually18/37 = 0.4865
Roulette Table Image
This ultimately gives the house the edge, so over the long run, everyone but the house loses.
The only way to win is to bet high, be lucky, and then STOP. This post is about generating a stopping rule. We can get around the house’s edge and generate an advantage by having a stopping rule, as well as the capital to provide a buffer for our losses.
I only focus on the so-called 50:50 bets (odds/evens or red/black). But the logic is identical for all the odds.
Chance of winning at first bet = 18/37 = 0.4865
If we lose, we can double down and bet again (twice the size of the first bet). Chance of winning on second bet is again 0.4865
So chance of losing on the first bet AND winning on the second bet is (1-0.4865) x 0.4865= 0.2498
So the chance of winning on EITHER the first or second bet is 0.4865 + 0.2498 = 0.7363
This means that if we want to win one million dollars, we can do it in two bets with 73.63% certainty, and need 3 million dollars to do so.
This can be formalized as follows;
P(y) = x[1-P(y-1)]+P(y-1)
Where;
y = the bet number (ie first or second or third bet etc)
P(y) = probability of winning on or before the yth bet, and
x = chance of winning = 0.4865
SO, if you want to win one million dollars, with 98% certainty, you need to have 63million dollars ready to go, and be prepared to make six bets!
Casinos get around this rule by having a maximum bet on the table. If you reach the max before you reach your stopping rule, you are screwed. I'm not sure what the max is in Torn Casino.
It tricks many people by including a slot for “zero” which does not count as odd, even, red or black.
So while betting red or even may seem like a 0.50 probability of success, it is actually18/37 = 0.4865
Roulette Table Image
This ultimately gives the house the edge, so over the long run, everyone but the house loses.
The only way to win is to bet high, be lucky, and then STOP. This post is about generating a stopping rule. We can get around the house’s edge and generate an advantage by having a stopping rule, as well as the capital to provide a buffer for our losses.
I only focus on the so-called 50:50 bets (odds/evens or red/black). But the logic is identical for all the odds.
Chance of winning at first bet = 18/37 = 0.4865
If we lose, we can double down and bet again (twice the size of the first bet). Chance of winning on second bet is again 0.4865
So chance of losing on the first bet AND winning on the second bet is (1-0.4865) x 0.4865= 0.2498
So the chance of winning on EITHER the first or second bet is 0.4865 + 0.2498 = 0.7363
This means that if we want to win one million dollars, we can do it in two bets with 73.63% certainty, and need 3 million dollars to do so.
This can be formalized as follows;
P(y) = x[1-P(y-1)]+P(y-1)
Where;
y = the bet number (ie first or second or third bet etc)
P(y) = probability of winning on or before the yth bet, and
x = chance of winning = 0.4865
| y | Cash to bet | running total | p(y) | Profit |
| 1 | 1 | 1 | 0.4865 | 1 |
| 2 | 2 | 3 | 0.7365 | 1 |
| 3 | 4 | 7 | 0.8647 | 1 |
| 4 | 8 | 15 | 0.9307 | 1 |
| 5 | 16 | 31 | 0.9643 | 1 |
| 6 | 32 | 63 | 0.9816 | 1 |
SO, if you want to win one million dollars, with 98% certainty, you need to have 63million dollars ready to go, and be prepared to make six bets!
Casinos get around this rule by having a maximum bet on the table. If you reach the max before you reach your stopping rule, you are screwed. I'm not sure what the max is in Torn Casino.